Unity model is distorting when animation is running
Weight painting defines how much a mesh follows each bone. With a weight of 1.0 the mesh follows the bone exactly, with a value of 0.5 the mesh will move half as much as the bone.

To me it looks like the hand has a weight of 1.0 but the sleeve has a weight of maybe 0.8 so it doesn't move with the bone the same amount as the hand.

With the shoulders this is a similar problem, due to having a disconnected mesh this tears the pieces apart. The edges of the two meshes that meet at the shoulder need to have matching weights so that they move the same amount. But then you shouldn't need to have a disconnected mesh in the middle of an asset that should be considered one object.

In blender, you can view the weights for selected vertices in the properties region (press N) while the models list of vertex groups is available in the mesh data properties.